Sockets

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A. Sockets

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Vasya has got many devices that work on electricity. He's got n supply-line filters to plug the devices, the i-th supply-line filter has a_i sockets.

Overall Vasya has got m devices and k electrical sockets in his flat, he can plug the devices or supply-line filters directly. Of course, he can plug the supply-line filter to any other supply-line filter. The device (or the supply-line filter) is considered plugged to electricity if it is either plugged to one of k electrical sockets, or if it is plugged to some supply-line filter that is in turn plugged to electricity.

What minimum number of supply-line filters from the given set will Vasya need to plug all the devices he has to electricity? Note that all devices and supply-line filters take one socket for plugging and that he can use one socket to plug either one device or one supply-line filter.

Input

The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 50) — the number of supply-line filters, the number of devices and the number of sockets that he can plug to directly, correspondingly. The second line contains n space-separated integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 50) — number a_i stands for the number of sockets on the i-th supply-line filter.

Output

Print a single number — the minimum number of supply-line filters that is needed to plug all the devices to electricity. If it is impossible to plug all the devices even using all the supply-line filters, print -1.

Sample test(s)

Input

3 5 3
3 1 2

Output

1

Input

4 7 2
3 3 2 4

Output

2

Input

5 5 1
1 3 1 2 1

Output

-1

Note

In the first test case he can plug the first supply-line filter directly to electricity. After he plug it, he get 5 (3 on the supply-line filter and 2 remaining sockets for direct plugging) available sockets to plug. Thus, one filter is enough to plug 5 devices.

One of the optimal ways in the second test sample is to plug the second supply-line filter directly and plug the fourth supply-line filter to one of the sockets in the second supply-line filter. Thus, he gets exactly 7 sockets, available to plug: one to plug to the electricity directly, 2 on the second supply-line filter, 4 on the fourth supply-line filter. There's no way he can plug 7 devices if he use one supply-line filter.

AC Code：

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

int main()
{
    int n, m, k, cnt;  //cnt为已通电插孔数
    int a[51], i;  //每个插座拥有的插孔数量
    while(cin >> n >> m >> k)
    {
        cnt = k;
        for(i = 0; i < n; i++)
            cin >> a[i];
        sort(a, a + i);
        while(cnt < m && i)
        {
            cnt += a[i - 1] - 1;
            i--;
        }
        if(cnt < m) cout << -1 << endl;
        else cout << n - i << endl;
    }
    return 0;
}